# Group theory Open problems that affect all finite groups.

What are the open problems in relation to everyone the finite groups?

The references will be appreciated. Here are two examples:

• Aschbacher-Guralnick conjecture. (AG1984 p.447): the number of conjugation classes of maximum subgroups of a finite group is at most its class number (that is, the number of classes of conjugation elements, or the number of complex representations irreducible up to equivalent).

• KANSAS. The problem of brown (B2000 Q.4; SW2016 p.760): Let $$G$$ be a finite group, $$mu$$ Be the Möbius function of your lattice subgroup. $$L (G)$$. Then the sum $$sum_ {H in L (G)} mu (H, G) | G: H |$$ It is different from zero.

There are two types of problems, those involving an upper / lower limit (such as the Aschbacher-Guralnick conjecture) and the "exact" ones, which do not involve any limits (such as K.S. Brown's problem). I guess the first type is much more abundant than the second, so for the first type, limit yourself to the main problems.